Two weeks earlier, the pilots voted to dump the union president and vice president.
But even if pilots vote down the offer, Mr. Parker is not likely to complain.
Two weeks ago, the leaders blocked an effort to have pilots vote on the airline's request for $295 million in cuts from that union.
Yesterday, United's pilots voted down by a 4-to-1 margin a tentative agreement that called for a cumulative wage increase of 10 percent over four years.
The union's executive council and the pilots must vote to approve the deal before it is official.
Delta's 10,000 pilots are currently voting on that contract.
It said some pilots who did not want union representation had voted for one union out of fear that another union would be elected.
But the union's board dismissed the idea, and four months later the pilots voted in James Sovich, the current president.
In that case, the pilots would vote on the deal about a month later.
The pilots are voting on $660 million in cost cuts.